Answer:
-1/18
Step-by-step explanation:
First, you have to change both fractions to have like denominators. The LCM of 2 and 9 is 18.
Second, you have to multiply -1/2 by 9/9 to get a denominator of 18. -1/2 x 9/9 is - 9/18.
Third, you have to multiply 4/9 by 2/2 to get a denominator of 18. 4/9 x 2/2 = 8/18.
Fourth, -9/18 + 8/18 = -1/18
Hope this helps!
Answer:
Option A. The volume of the sphere is multiplied by 1/343.
Step-by-step explanation:
The volume of a sphere can be obtained by the following formula:
V = 4/3πr^3
Let the initial volume (V1) of the sphere be:
V1 = 4/3πr^3 = (4πr^3)/3
Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:
V2 = 4/3 x π x (1/7r)^3
V2 = 4/3 x π x 1/343r^3
V2 = (4πr^3)/1029
Now we determine the ratio of V2 : V1 as shown below:
V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3
V2/V1 = (4πr^3)/1029 × 3/(4πr^3)
V2/V1 = 3/1029
V2/V1 = 1/343
V2 = 1/343 x V1
Therefore, the volume of the sphere is multiplied by 1/343.
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
brainly.com/question/18760518
Step 1. Identify the unit you have
Step 2. Identify the unit you want to covert to
Step 3. Count the number of units between them
(<span>If </span>you<span> are going from a larger </span>unit<span> to a smaller </span>unit<span>, </span>you<span> multiply by 10 successively.)</span>
Hello,
2x²+x-14=0
Δ=1+4*14*2=113
x=(-1-√113)/4=-2,8839...≈-2.88
or x=(-1+√113)/4=2,40753≈2.41
